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    Question

    If cos θ = (4x² – 1)/(1 + 4x²) then find the value of

    sin q.
    A 4x/(1 - 4x²) Correct Answer Incorrect Answer
    B 3x/(1 + 4x²) Correct Answer Incorrect Answer
    C 2x/(4x² - 1) Correct Answer Incorrect Answer
    D 4x/(1+ 4x²) Correct Answer Incorrect Answer

    Solution

    We know that cos A = (Base/Hypotenuse)

    So, Base of the right-angled triangle is (4x 2  - 1) units.

    Hypotenuse of the right-angled triangle is (1 + 4x 2 ) units.

    Using Pythagoras theorem, we get,

    (Perpendicular)  2  + (Base)  2  = (Hypotenuse)  2

    Or, (Perpendicular)  2  + (4x 2  - 1)  2  = (1 + 4x 2 )  2

    Or, (Perpendicular)  2  = (1 + 4x 2 )  2  - (4x 2  - 1)  2

    We know that, a 2  - b 2  = (a + b) X (a - b) .

    Or, (Perpendicular)  2  = (1 + 4x 2  + 4x 2  - 1) X (1 + 4x 2  - 4x 2  + 1)

    Or, (Perpendicular)  2  = 8x 2  X 2 = (16x 2 )

    Since, perpendicular of a triangle cannot be negative.

    So, Perpendicular = '4x' units

    We know that sine A = (Perpendicular/Hypotenuse)

    So, sin θ = 4x/(1 + 4x²)

    Practice Next

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